when each edge of a cube is decreased by 1 cm, its volume is decreased by 91 cm^3 .Find the length of the a side of the original cube. HELP ME PLZ PEOPLE!!!!!!!!!!!!!!!!!!
Answers
Answer:
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Step-by-step explanation:
Let the length of the cube be x
Length after 2cm increase = x + 2
Find the original volume:
Volume = Length³
Volume = x³
Find the new volume:
Volume = Length³
Volume = (x + 2)³
Form equation and solve for x:
The volume is decreased by 91 cm
(x + 2)³ - x³ = 91
x³ +6x² +12x + 8 - x³ =91
6x² +12x - 480 = 0
x² +2x - 80 = 0
(x - 8)(x + 10) = 0
x = 8 or x = - 10 (rejected, x cannot be negative)
Find the new length:
New length = 8 + 2 = 10 cm
Answer: The new length is 10 cm
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Answer:
30cm or 90cm
Step-by-step explanation:
Let the length of edge of a cube be a cm.
It's volume = a^3 cm^3
Each edge of cube is decreased by 1 cm.
So, new length of edge of cube will be (a-1) cm.
Hence, the volume becomes (a-1)^3 cm^3.
It's given that, volume is decreased by 91 cm^3
i.e, (a-1)^3 = a^3 - 91
⇒ a^3 - 1 - 3a^2 + 3a = a^3 - 91
⇒ 3a^2 - 3a = 91 - 1
⇒ 3a (a - 1) = 90
⇒ 3a = 90 and a = 30
⇒ a - 1 = 90 and a = 91
Therefore, the length of the side of original cube is 30 or 90 cm.